Geodesic
Convergence of sequences of iterates of random-valued vector functions
Rafał Kapica1
1 Institute of Mathematics Silesian University Bankowa 14 40-007 Katowice, Poland
Colloquium Mathematicum, Tome 97 (2003) no. 1, pp. 1-6

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Given a probability space $({\mit \Omega },{{\mathcal A}},P)$ and a closed subset $X$ of a Banach lattice, we consider functions $f:X\times {\mit \Omega }\to X$ and their iterates $f^n:X\times {\mit \Omega }^{{{\mathbb N}}}\to X$ defined by $f^1(x,\omega )=f(x,\omega _1)$, $f^{n+1}(x,\omega )=f(f^n(x,\omega ),\omega _{n+1})$, and obtain theorems on the convergence (a.s. and in $L^1$) of the sequence $(f^n(x,\cdot ))$.
DOI : 10.4064/cm97-1-1
Keywords: given probability space mit omega mathcal closed subset banach lattice consider functions times mit omega their iterates times mit omega mathbb defined omega omega omega x omega omega obtain theorems convergence sequence cdot

Rafał Kapica 1

1 Institute of Mathematics Silesian University Bankowa 14 40-007 Katowice, Poland 
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Rafał Kapica. Convergence of sequences of iterates
 of random-valued vector functions. Colloquium Mathematicum, Tome 97 (2003) no. 1, pp. 1-6. doi: 10.4064/cm97-1-1

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